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In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. (Contains 6 figures.)

The authors use multiple-sample longitudinal data from different test batteries to examine propositions about changes in constructs over the life span. The data come from 3 classic studies on intellectual abilities in which, in combination, 441 persons were repeatedly measured as many as 16 times over 70 years. They measured cognitive constructs of vocabulary and memory using 8 age-appropriate intelligence test batteries and explore possible linkage of these scales using item response theory (IRT). They simultaneously estimated the parameters of both IRT and latent curve models based on a joint model likelihood approach (i.e., NLMIXED and WINBUGS). They included group differences in the model to examine potential interindividual differences in levels and change. The resulting longitudinal invariant Rasch test analyses lead to a few new methodological suggestions for dealing with repeated constructs based on changing measurements in developmental studies. (Contains 5 tables and 4 figures.)